! Gathering
! Gradient/hessian/criterion for the localization:
! They are chosen in function of the localization method
! Gradient:
! qp_edit :
! | localization_method | method for the localization |
! Input:
! | tmp_n | integer | Number of parameters in the MO subspace |
! | tmp_list_size | integer | Number of MOs in the mo_class we want to localize |
! | tmp_list(tmp_list_size) | integer | MOs in the mo_class |
! Output:
! | v_grad(tmp_n) | double precision | Gradient in the subspace |
! | max_elem | double precision | Maximal element in the gradient |
! | norm_grad | double precision | Norm of the gradient |
subroutine gradient_localization(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_grad)
include 'pi.h'
implicit none
BEGIN_DOC
! Compute the gradient of the chosen localization method
END_DOC
integer, intent(in) :: tmp_n, tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: v_grad(tmp_n), max_elem, norm_grad
if (localization_method == 'boys') then
call gradient_FB_omp(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_grad)
!call gradient_FB(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_grad)
elseif (localization_method== 'pipek') then
call gradient_PM(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_grad)
else
print*,'Unkown method:'//localization_method
call abort
endif
end
! Hessian:
! Output:
! | H(tmp_n,tmp_n) | double precision | Gradient in the subspace |
! | max_elem | double precision | Maximal element in the gradient |
! | norm_grad | double precision | Norm of the gradient |
subroutine hessian_localization(tmp_n, tmp_list_size, tmp_list, H)
include 'pi.h'
implicit none
BEGIN_DOC
! Compute the diagonal hessian of the chosen localization method
END_DOC
integer, intent(in) :: tmp_n, tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: H(tmp_n)
if (localization_method == 'boys') then
call hessian_FB_omp(tmp_n, tmp_list_size, tmp_list, H)
!call hessian_FB(tmp_n, tmp_list_size, tmp_list, H) ! non OMP for debugging
elseif (localization_method == 'pipek') then
call hessian_PM(tmp_n, tmp_list_size, tmp_list, H)
else
print*,'Unkown method: '//localization_method
call abort
endif
end
! Criterion:
! Output:
! | criterion | double precision | Criterion for the orbital localization |
subroutine criterion_localization(tmp_list_size, tmp_list,criterion)
include 'pi.h'
implicit none
BEGIN_DOC
! Compute the localization criterion of the chosen localization method
END_DOC
integer, intent(in) :: tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: criterion
if (localization_method == 'boys') then
call criterion_FB(tmp_list_size, tmp_list, criterion)
elseif (localization_method == 'pipek') then
!call criterion_PM(tmp_list_size, tmp_list,criterion)
call criterion_PM_v3(tmp_list_size, tmp_list, criterion)
else
print*,'Unkown method: '//localization_method
call abort
endif
end
! Subroutine to update the datas needed for the localization
subroutine update_data_localization()
include 'pi.h'
implicit none
if (localization_method == 'boys') then
! Update the dipoles
call ao_to_mo_no_sym(ao_dipole_x, ao_num, mo_dipole_x, mo_num)
call ao_to_mo_no_sym(ao_dipole_y, ao_num, mo_dipole_y, mo_num)
call ao_to_mo_no_sym(ao_dipole_z, ao_num, mo_dipole_z, mo_num)
elseif (localization_method == 'pipek') then
! Nothing required
else
print*,'Unkown method: '//localization_method
call abort
endif
end
! Angles:
! Output:
! | tmp_m_x(tmp_list_size, tmp_list_size) | double precision | Angles for the rotations in the subspace |
! | max_elem | double precision | Maximal angle |
subroutine theta_localization(tmp_list, tmp_list_size, tmp_m_x, max_elem)
include 'pi.h'
implicit none
BEGIN_DOC
! Compute the rotation angles between the MOs for the chosen localization method
END_DOC
integer, intent(in) :: tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: tmp_m_x(tmp_list_size,tmp_list_size), max_elem
if (localization_method == 'boys') then
call theta_FB(tmp_list, tmp_list_size, tmp_m_x, max_elem)
elseif (localization_method== 'pipek') then
call theta_PM(tmp_list, tmp_list_size, tmp_m_x, max_elem)
else
print*,'Unkown method: '//localization_method
call abort
endif
end
! Gradient
! Input:
! | tmp_n | integer | Number of parameters in the MO subspace |
! | tmp_list_size | integer | Number of MOs in the mo_class we want to localize |
! | tmp_list(tmp_list_size) | integer | MOs in the mo_class |
! Output:
! | v_grad(tmp_n) | double precision | Gradient in the subspace |
! | max_elem | double precision | Maximal element in the gradient |
! | norm_grad | double precision | Norm of the gradient |
! Internal:
! | m_grad(tmp_n,tmp_n) | double precision | Gradient in the matrix form |
! | i,j,k | integer | indexes in the full space |
! | tmp_i,tmp_j,tmp_k | integer | indexes in the subspace |
! | t* | double precision | to compute the time |
subroutine gradient_FB(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_grad)
implicit none
BEGIN_DOC
! Compute the gradient for the Foster-Boys localization
END_DOC
integer, intent(in) :: tmp_n, tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: v_grad(tmp_n), max_elem, norm_grad
double precision, allocatable :: m_grad(:,:)
integer :: i,j,k,tmp_i,tmp_j,tmp_k
double precision :: t1, t2, t3
print*,''
print*,'---gradient_FB---'
call wall_time(t1)
! Allocation
allocate(m_grad(tmp_list_size, tmp_list_size))
! Calculation
do tmp_j = 1, tmp_list_size
j = tmp_list(tmp_j)
do tmp_i = 1, tmp_list_size
i = tmp_list(tmp_i)
m_grad(tmp_i,tmp_j) = 4d0 * mo_dipole_x(i,j) * (mo_dipole_x(i,i) - mo_dipole_x(j,j)) &
+4d0 * mo_dipole_y(i,j) * (mo_dipole_y(i,i) - mo_dipole_y(j,j)) &
+4d0 * mo_dipole_z(i,j) * (mo_dipole_z(i,i) - mo_dipole_z(j,j))
enddo
enddo
! 2D -> 1D
do tmp_k = 1, tmp_n
call vec_to_mat_index(tmp_k,tmp_i,tmp_j)
v_grad(tmp_k) = m_grad(tmp_i,tmp_j)
enddo
! Maximum element in the gradient
max_elem = 0d0
do tmp_k = 1, tmp_n
if (ABS(v_grad(tmp_k)) > max_elem) then
max_elem = ABS(v_grad(tmp_k))
endif
enddo
! Norm of the gradient
norm_grad = 0d0
do tmp_k = 1, tmp_n
norm_grad = norm_grad + v_grad(tmp_k)**2
enddo
norm_grad = dsqrt(norm_grad)
print*, 'Maximal element in the gradient:', max_elem
print*, 'Norm of the gradient:', norm_grad
! Deallocation
deallocate(m_grad)
call wall_time(t2)
t3 = t2 - t1
print*,'Time in gradient_FB:', t3
print*,'---End gradient_FB---'
end subroutine
! Gradient (OMP)
subroutine gradient_FB_omp(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_grad)
use omp_lib
implicit none
BEGIN_DOC
! Compute the gradient for the Foster-Boys localization
END_DOC
integer, intent(in) :: tmp_n, tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: v_grad(tmp_n), max_elem, norm_grad
double precision, allocatable :: m_grad(:,:)
integer :: i,j,k,tmp_i,tmp_j,tmp_k
double precision :: t1, t2, t3
print*,''
print*,'---gradient_FB_omp---'
call wall_time(t1)
! Allocation
allocate(m_grad(tmp_list_size, tmp_list_size))
! Initialization omp
call omp_set_max_active_levels(1)
!$OMP PARALLEL &
!$OMP PRIVATE(i,j,tmp_i,tmp_j,tmp_k) &
!$OMP SHARED(tmp_n,tmp_list_size,m_grad,v_grad,mo_dipole_x,mo_dipole_y,mo_dipole_z,tmp_list) &
!$OMP DEFAULT(NONE)
! Calculation
!$OMP DO
do tmp_j = 1, tmp_list_size
j = tmp_list(tmp_j)
do tmp_i = 1, tmp_list_size
i = tmp_list(tmp_i)
m_grad(tmp_i,tmp_j) = 4d0 * mo_dipole_x(i,j) * (mo_dipole_x(i,i) - mo_dipole_x(j,j)) &
+4d0 * mo_dipole_y(i,j) * (mo_dipole_y(i,i) - mo_dipole_y(j,j)) &
+4d0 * mo_dipole_z(i,j) * (mo_dipole_z(i,i) - mo_dipole_z(j,j))
enddo
enddo
!$OMP END DO
! 2D -> 1D
!$OMP DO
do tmp_k = 1, tmp_n
call vec_to_mat_index(tmp_k,tmp_i,tmp_j)
v_grad(tmp_k) = m_grad(tmp_i,tmp_j)
enddo
!$OMP END DO
!$OMP END PARALLEL
call omp_set_max_active_levels(4)
! Maximum element in the gradient
max_elem = 0d0
do tmp_k = 1, tmp_n
if (ABS(v_grad(tmp_k)) > max_elem) then
max_elem = ABS(v_grad(tmp_k))
endif
enddo
! Norm of the gradient
norm_grad = 0d0
do tmp_k = 1, tmp_n
norm_grad = norm_grad + v_grad(tmp_k)**2
enddo
norm_grad = dsqrt(norm_grad)
print*, 'Maximal element in the gradient:', max_elem
print*, 'Norm of the gradient:', norm_grad
! Deallocation
deallocate(m_grad)
call wall_time(t2)
t3 = t2 - t1
print*,'Time in gradient_FB_omp:', t3
print*,'---End gradient_FB_omp---'
end subroutine
! Hessian
! Output:
! | H(tmp_n,tmp_n) | double precision | Gradient in the subspace |
! | max_elem | double precision | Maximal element in the gradient |
! | norm_grad | double precision | Norm of the gradient |
! Internal:
! Internal:
! | beta(tmp_n,tmp_n) | double precision | beta in the documentation below to compute the hesian |
! | i,j,k | integer | indexes in the full space |
! | tmp_i,tmp_j,tmp_k | integer | indexes in the subspace |
! | t* | double precision | to compute the time |
subroutine hessian_FB(tmp_n, tmp_list_size, tmp_list, H)
implicit none
BEGIN_DOC
! Compute the diagonal hessian for the Foster-Boys localization
END_DOC
integer, intent(in) :: tmp_n, tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: H(tmp_n)
double precision, allocatable :: beta(:,:)
integer :: i,j,tmp_k,tmp_i, tmp_j
double precision :: max_elem, t1,t2,t3
print*,''
print*,'---hessian_FB---'
call wall_time(t1)
! Allocation
allocate(beta(tmp_list_size,tmp_list_size))
! Calculation
do tmp_j = 1, tmp_list_size
j = tmp_list(tmp_j)
do tmp_i = 1, tmp_list_size
i = tmp_list(tmp_i)
beta(tmp_i,tmp_j) = (mo_dipole_x(i,i) - mo_dipole_x(j,j))**2 - 4d0 * mo_dipole_x(i,j)**2 &
+(mo_dipole_y(i,i) - mo_dipole_y(j,j))**2 - 4d0 * mo_dipole_y(i,j)**2 &
+(mo_dipole_z(i,i) - mo_dipole_z(j,j))**2 - 4d0 * mo_dipole_z(i,j)**2
enddo
enddo
! Diagonal of the hessian
H = 0d0
do tmp_k = 1, tmp_n
call vec_to_mat_index(tmp_k,tmp_i,tmp_j)
H(tmp_k) = 4d0 * beta(tmp_i, tmp_j)
enddo
! Deallocation
deallocate(beta)
call wall_time(t2)
t3 = t2 - t1
print*,'Time in hessian_FB:', t3
print*,'---End hessian_FB---'
end subroutine
! Hessian (OMP)
subroutine hessian_FB_omp(tmp_n, tmp_list_size, tmp_list, H)
implicit none
BEGIN_DOC
! Compute the diagonal hessian for the Foster-Boys localization
END_DOC
integer, intent(in) :: tmp_n, tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: H(tmp_n)
double precision, allocatable :: beta(:,:)
integer :: i,j,tmp_k,tmp_i,tmp_j
double precision :: max_elem, t1,t2,t3
print*,''
print*,'---hessian_FB_omp---'
call wall_time(t1)
! Allocation
allocate(beta(tmp_list_size,tmp_list_size))
! Initialization omp
call omp_set_max_active_levels(1)
!$OMP PARALLEL &
!$OMP PRIVATE(i,j,tmp_i,tmp_j,tmp_k) &
!$OMP SHARED(tmp_n,tmp_list_size,beta,H,mo_dipole_x,mo_dipole_y,mo_dipole_z,tmp_list) &
!$OMP DEFAULT(NONE)
! Calculation
!$OMP DO
do tmp_j = 1, tmp_list_size
j = tmp_list(tmp_j)
do tmp_i = 1, tmp_list_size
i = tmp_list(tmp_i)
beta(tmp_i,tmp_j) = (mo_dipole_x(i,i) - mo_dipole_x(j,j))**2 - 4d0 * mo_dipole_x(i,j)**2 &
+(mo_dipole_y(i,i) - mo_dipole_y(j,j))**2 - 4d0 * mo_dipole_y(i,j)**2 &
+(mo_dipole_z(i,i) - mo_dipole_z(j,j))**2 - 4d0 * mo_dipole_z(i,j)**2
enddo
enddo
!$OMP END DO
! Initialization
!$OMP DO
do i = 1, tmp_n
H(i) = 0d0
enddo
!$OMP END DO
! Diagonalm of the hessian
!$OMP DO
do tmp_k = 1, tmp_n
call vec_to_mat_index(tmp_k,tmp_i,tmp_j)
H(tmp_k) = 4d0 * beta(tmp_i, tmp_j)
enddo
!$OMP END DO
!$OMP END PARALLEL
call omp_set_max_active_levels(4)
! Deallocation
deallocate(beta)
call wall_time(t2)
t3 = t2 - t1
print*,'Time in hessian_FB_omp:', t3
print*,'---End hessian_FB_omp---'
end subroutine
! Gradient v1
subroutine grad_pipek(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_grad)
implicit none
BEGIN_DOC
! Compute gradient for the Pipek-Mezey localization
END_DOC
integer, intent(in) :: tmp_n, tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: v_grad(tmp_n), max_elem, norm_grad
double precision, allocatable :: m_grad(:,:), tmp_int(:,:)
integer :: i,j,k,tmp_i,tmp_j,tmp_k, a, b, mu ,rho
! Allocation
allocate(m_grad(tmp_list_size, tmp_list_size), tmp_int(tmp_list_size, tmp_list_size))
! Initialization
m_grad = 0d0
do a = 1, nucl_num ! loop over the nuclei
tmp_int = 0d0 ! Initialization for each nuclei
! Loop over the MOs of the a given mo_class to compute <i|P_a|j>
do tmp_j = 1, tmp_list_size
j = tmp_list(tmp_j)
do tmp_i = 1, tmp_list_size
i = tmp_list(tmp_i)
do rho = 1, ao_num ! loop over all the AOs
do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
mu = nucl_aos(a,b) ! AO centered on atom a
tmp_int(tmp_i,tmp_j) = tmp_int(tmp_i,tmp_j) + 0.5d0 * (mo_coef(rho,i) * ao_overlap(rho,mu) * mo_coef(mu,j) &
+ mo_coef(mu,i) * ao_overlap(mu,rho) * mo_coef(rho,j))
enddo
enddo
enddo
enddo
! Gradient
do tmp_j = 1, tmp_list_size
do tmp_i = 1, tmp_list_size
m_grad(tmp_i,tmp_j) = m_grad(tmp_i,tmp_j) + 4d0 * tmp_int(tmp_i,tmp_j) * (tmp_int(tmp_i,tmp_i) - tmp_int(tmp_j,tmp_j))
enddo
enddo
enddo
! 2D -> 1D
do tmp_k = 1, tmp_n
call vec_to_mat_index(tmp_k,tmp_i,tmp_j)
v_grad(tmp_k) = m_grad(tmp_i,tmp_j)
enddo
! Maximum element in the gradient
max_elem = 0d0
do tmp_k = 1, tmp_n
if (ABS(v_grad(tmp_k)) > max_elem) then
max_elem = ABS(v_grad(tmp_k))
endif
enddo
! Norm of the gradient
norm_grad = 0d0
do tmp_k = 1, tmp_n
norm_grad = norm_grad + v_grad(tmp_k)**2
enddo
norm_grad = dsqrt(norm_grad)
print*, 'Maximal element in the gradient:', max_elem
print*, 'Norm of the gradient:', norm_grad
! Deallocation
deallocate(m_grad,tmp_int)
end subroutine grad_pipek
! Gradient
! The gradient is
! \begin{align*}
! \left. \frac{\partial \mathcal{P} (\theta)}{\partial \theta} \right|_{\theta=0}= \gamma^{PM}
! \end{align*}
! with
! \begin{align*}
! \gamma_{st}^{PM} = \sum_{A=1}^N <s|P_A|t> \left[ <s| P_A |s> - <t|P_A|t> \right]
! \end{align*}
! \begin{align*}
! <s|P_A|t> = \frac{1}{2} \sum_{\rho} \sum_{\mu \in A} \left[ c_{\rho}^{s*} S_{\rho \nu} c_{\mu}^{t} +c_{\mu}^{s*} S_{\mu \rho} c_{\rho}^t \right]
! \end{align*}
! $\sum_{\rho}$ -> sum over all the AOs
! $\sum_{\mu \in A}$ -> sum over the AOs which belongs to atom A
! $c^t$ -> expansion coefficient of orbital |t>
! Input:
! | tmp_n | integer | Number of parameters in the MO subspace |
! | tmp_list_size | integer | Number of MOs in the mo_class we want to localize |
! | tmp_list(tmp_list_size) | integer | MOs in the mo_class |
! Output:
! | v_grad(tmp_n) | double precision | Gradient in the subspace |
! | max_elem | double precision | Maximal element in the gradient |
! | norm_grad | double precision | Norm of the gradient |
! Internal:
! | m_grad(tmp_list_size,tmp_list_size) | double precision | Gradient in a 2D array |
! | tmp_int(tmp_list_size,tmp_list_size) | | Temporary array to store the integrals |
! | tmp_accu(tmp_list_size,tmp_list_size) | | Temporary array to store a matrix |
! | | | product and compute tmp_int |
! | CS(tmp_list_size,ao_num) | | Array to store the result of mo_coef * ao_overlap |
! | tmp_mo_coef(ao_num,tmp_list_size) | | Array to store just the useful MO coefficients |
! | | | depending of the mo_class |
! | tmp_mo_coef2(nucl_n_aos(a),tmp_list_size) | | Array to store just the useful MO coefficients |
! | | | depending of the nuclei |
! | tmp_CS(tmp_list_size,nucl_n_aos(a)) | | Array to store just the useful mo_coef * ao_overlap |
! | | | values depending of the nuclei |
! | a | | index to loop over the nuclei |
! | b | | index to loop over the AOs which belongs to the nuclei a |
! | mu | | index to refer to an AO which belongs to the nuclei a |
! | rho | | index to loop over all the AOs |
subroutine gradient_PM(tmp_n, tmp_list_size, tmp_list, v_grad, max_elem, norm_grad)
implicit none
BEGIN_DOC
! Compute gradient for the Pipek-Mezey localization
END_DOC
integer, intent(in) :: tmp_n, tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: v_grad(tmp_n), max_elem, norm_grad
double precision, allocatable :: m_grad(:,:), tmp_int(:,:), CS(:,:), tmp_mo_coef(:,:), tmp_mo_coef2(:,:),tmp_accu(:,:),tmp_CS(:,:)
integer :: i,j,k,tmp_i,tmp_j,tmp_k, a, b, mu ,rho
double precision :: t1,t2,t3
print*,''
print*,'---gradient_PM---'
call wall_time(t1)
! Allocation
allocate(m_grad(tmp_list_size, tmp_list_size), tmp_int(tmp_list_size, tmp_list_size),tmp_accu(tmp_list_size, tmp_list_size))
allocate(CS(tmp_list_size,ao_num),tmp_mo_coef(ao_num,tmp_list_size))
! submatrix of the mo_coef
do tmp_i = 1, tmp_list_size
i = tmp_list(tmp_i)
do j = 1, ao_num
tmp_mo_coef(j,tmp_i) = mo_coef(j,i)
enddo
enddo
call dgemm('T','N',tmp_list_size,ao_num,ao_num,1d0,tmp_mo_coef,size(tmp_mo_coef,1),ao_overlap,size(ao_overlap,1),0d0,CS,size(CS,1))
m_grad = 0d0
do a = 1, nucl_num ! loop over the nuclei
tmp_int = 0d0
!do tmp_j = 1, tmp_list_size
! do tmp_i = 1, tmp_list_size
! do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
! mu = nucl_aos(a,b)
! tmp_int(tmp_i,tmp_j) = tmp_int(tmp_i,tmp_j) + 0.5d0 * (CS(tmp_i,mu) * tmp_mo_coef(mu,tmp_j) + tmp_mo_coef(mu,tmp_i) * CS(tmp_j,mu))
! ! (mo_coef(rho,i) * ao_overlap(rho,mu) * mo_coef(mu,j) &
! !+ mo_coef(mu,i) * ao_overlap(mu,rho) * mo_coef(rho,j))
! enddo
! enddo
!enddo
allocate(tmp_mo_coef2(nucl_n_aos(a),tmp_list_size),tmp_CS(tmp_list_size,nucl_n_aos(a)))
do tmp_i = 1, tmp_list_size
do b = 1, nucl_n_aos(a)
mu = nucl_aos(a,b)
tmp_mo_coef2(b,tmp_i) = tmp_mo_coef(mu,tmp_i)
enddo
enddo
do b = 1, nucl_n_aos(a)
mu = nucl_aos(a,b)
do tmp_i = 1, tmp_list_size
tmp_CS(tmp_i,b) = CS(tmp_i,mu)
enddo
enddo
call dgemm('N','N',tmp_list_size,tmp_list_size,nucl_n_aos(a),1d0,tmp_CS,size(tmp_CS,1),tmp_mo_coef2,size(tmp_mo_coef2,1),0d0,tmp_accu,size(tmp_accu,1))
do tmp_j = 1, tmp_list_size
do tmp_i = 1, tmp_list_size
tmp_int(tmp_i,tmp_j) = 0.5d0 * (tmp_accu(tmp_i,tmp_j) + tmp_accu(tmp_j,tmp_i))
enddo
enddo
deallocate(tmp_mo_coef2,tmp_CS)
do tmp_j = 1, tmp_list_size
do tmp_i = 1, tmp_list_size
m_grad(tmp_i,tmp_j) = m_grad(tmp_i,tmp_j) + 4d0 * tmp_int(tmp_i,tmp_j) * (tmp_int(tmp_i,tmp_i) - tmp_int(tmp_j,tmp_j))
enddo
enddo
enddo
! 2D -> 1D
do tmp_k = 1, tmp_n
call vec_to_mat_index(tmp_k,tmp_i,tmp_j)
v_grad(tmp_k) = m_grad(tmp_i,tmp_j)
enddo
! Maximum element in the gradient
max_elem = 0d0
do tmp_k = 1, tmp_n
if (ABS(v_grad(tmp_k)) > max_elem) then
max_elem = ABS(v_grad(tmp_k))
endif
enddo
! Norm of the gradient
norm_grad = 0d0
do tmp_k = 1, tmp_n
norm_grad = norm_grad + v_grad(tmp_k)**2
enddo
norm_grad = dsqrt(norm_grad)
print*, 'Maximal element in the gradient:', max_elem
print*, 'Norm of the gradient:', norm_grad
! Deallocation
deallocate(m_grad,tmp_int,CS,tmp_mo_coef)
call wall_time(t2)
t3 = t2 - t1
print*,'Time in gradient_PM:', t3
print*,'---End gradient_PM---'
end
! Hessian v1
subroutine hess_pipek(tmp_n, tmp_list_size, tmp_list, H)
implicit none
BEGIN_DOC
! Compute diagonal hessian for the Pipek-Mezey localization
END_DOC
integer, intent(in) :: tmp_n, tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: H(tmp_n)
double precision, allocatable :: beta(:,:),tmp_int(:,:)
integer :: i,j,tmp_k,tmp_i, tmp_j, a,b,rho,mu
double precision :: max_elem
! Allocation
allocate(beta(tmp_list_size,tmp_list_size),tmp_int(tmp_list_size,tmp_list_size))
beta = 0d0
do a = 1, nucl_num
tmp_int = 0d0
do tmp_j = 1, tmp_list_size
j = tmp_list(tmp_j)
do tmp_i = 1, tmp_list_size
i = tmp_list(tmp_i)
do rho = 1, ao_num
do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
mu = nucl_aos(a,b)
tmp_int(tmp_i,tmp_j) = tmp_int(tmp_i,tmp_j) + 0.5d0 * (mo_coef(rho,i) * ao_overlap(rho,mu) * mo_coef(mu,j) &
+ mo_coef(mu,i) * ao_overlap(mu,rho) * mo_coef(rho,j))
enddo
enddo
enddo
enddo
! Calculation
do tmp_j = 1, tmp_list_size
do tmp_i = 1, tmp_list_size
beta(tmp_i,tmp_j) = beta(tmp_i, tmp_j) + (tmp_int(tmp_i,tmp_i) - tmp_int(tmp_j,tmp_j))**2 - 4d0 * tmp_int(tmp_i,tmp_j)**2
enddo
enddo
enddo
H = 0d0
do tmp_k = 1, tmp_n
call vec_to_mat_index(tmp_k,tmp_i,tmp_j)
H(tmp_k) = 4d0 * beta(tmp_i, tmp_j)
enddo
! Deallocation
deallocate(beta,tmp_int)
end
! Hessian
! The hessian is
! \begin{align*}
! \left. \frac{\partial^2 \mathcal{P} (\theta)}{\partial \theta^2}\right|_{\theta=0} = 4 \beta^{PM}
! \end{align*}
! \begin{align*}
! \beta_{st}^{PM} = \sum_{A=1}^N \left( <s|P_A|t>^2 - \frac{1}{4} \left[<s|P_A|s> - <t|P_A|t> \right]^2 \right)
! \end{align*}
! with
! \begin{align*}
! <s|P_A|t> = \frac{1}{2} \sum_{\rho} \sum_{\mu \in A} \left[ c_{\rho}^{s*} S_{\rho \nu} c_{\mu}^{t} +c_{\mu}^{s*} S_{\mu \rho} c_{\rho}^t \right]
! \end{align*}
! $\sum_{\rho}$ -> sum over all the AOs
! $\sum_{\mu \in A}$ -> sum over the AOs which belongs to atom A
! $c^t$ -> expansion coefficient of orbital |t>
subroutine hessian_PM(tmp_n, tmp_list_size, tmp_list, H)
implicit none
BEGIN_DOC
! Compute diagonal hessian for the Pipek-Mezey localization
END_DOC
integer, intent(in) :: tmp_n, tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: H(tmp_n)
double precision, allocatable :: beta(:,:),tmp_int(:,:),CS(:,:),tmp_mo_coef(:,:),tmp_mo_coef2(:,:),tmp_accu(:,:),tmp_CS(:,:)
integer :: i,j,tmp_k,tmp_i, tmp_j, a,b,rho,mu
double precision :: max_elem, t1,t2,t3
print*,''
print*,'---hessian_PM---'
call wall_time(t1)
! Allocation
allocate(beta(tmp_list_size,tmp_list_size),tmp_int(tmp_list_size,tmp_list_size),tmp_accu(tmp_list_size,tmp_list_size))
allocate(CS(tmp_list_size,ao_num),tmp_mo_coef(ao_num,tmp_list_size))
beta = 0d0
do tmp_i = 1, tmp_list_size
i = tmp_list(tmp_i)
do j = 1, ao_num
tmp_mo_coef(j,tmp_i) = mo_coef(j,i)
enddo
enddo
call dgemm('T','N',tmp_list_size,ao_num,ao_num,1d0,tmp_mo_coef,size(tmp_mo_coef,1),ao_overlap,size(ao_overlap,1),0d0,CS,size(CS,1))
do a = 1, nucl_num ! loop over the nuclei
tmp_int = 0d0
!do tmp_j = 1, tmp_list_size
! do tmp_i = 1, tmp_list_size
! do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
! mu = nucl_aos(a,b)
! tmp_int(tmp_i,tmp_j) = tmp_int(tmp_i,tmp_j) + 0.5d0 * (CS(tmp_i,mu) * tmp_mo_coef(mu,tmp_j) + tmp_mo_coef(mu,tmp_i) * CS(tmp_j,mu))
! ! (mo_coef(rho,i) * ao_overlap(rho,mu) * mo_coef(mu,j) &
! !+ mo_coef(mu,i) * ao_overlap(mu,rho) * mo_coef(rho,j))
! enddo
! enddo
!enddo
allocate(tmp_mo_coef2(nucl_n_aos(a),tmp_list_size),tmp_CS(tmp_list_size,nucl_n_aos(a)))
do tmp_i = 1, tmp_list_size
do b = 1, nucl_n_aos(a)
mu = nucl_aos(a,b)
tmp_mo_coef2(b,tmp_i) = tmp_mo_coef(mu,tmp_i)
enddo
enddo
do b = 1, nucl_n_aos(a)
mu = nucl_aos(a,b)
do tmp_i = 1, tmp_list_size
tmp_CS(tmp_i,b) = CS(tmp_i,mu)
enddo
enddo
call dgemm('N','N',tmp_list_size,tmp_list_size,nucl_n_aos(a),1d0,tmp_CS,size(tmp_CS,1),tmp_mo_coef2,size(tmp_mo_coef2,1),0d0,tmp_accu,size(tmp_accu,1))
do tmp_j = 1, tmp_list_size
do tmp_i = 1, tmp_list_size
tmp_int(tmp_i,tmp_j) = 0.5d0 * (tmp_accu(tmp_i,tmp_j) + tmp_accu(tmp_j,tmp_i))
enddo
enddo
deallocate(tmp_mo_coef2,tmp_CS)
! Calculation
do tmp_j = 1, tmp_list_size
do tmp_i = 1, tmp_list_size
beta(tmp_i,tmp_j) = beta(tmp_i, tmp_j) + (tmp_int(tmp_i,tmp_i) - tmp_int(tmp_j,tmp_j))**2 - 4d0 * tmp_int(tmp_i,tmp_j)**2
enddo
enddo
enddo
H = 0d0
do tmp_k = 1, tmp_n
call vec_to_mat_index(tmp_k,tmp_i,tmp_j)
H(tmp_k) = 4d0 * beta(tmp_i, tmp_j)
enddo
! Deallocation
deallocate(beta,tmp_int)
call wall_time(t2)
t3 = t2 - t1
print*,'Time in hessian_PM:', t3
print*,'---End hessian_PM---'
end
! Criterion PM (old)
subroutine compute_crit_pipek(criterion)
implicit none
BEGIN_DOC
! Compute the Pipek-Mezey localization criterion
END_DOC
double precision, intent(out) :: criterion
double precision, allocatable :: tmp_int(:,:)
integer :: i,j,k,tmp_i,tmp_j,tmp_k, a, b, mu ,rho
! Allocation
allocate(tmp_int(mo_num, mo_num))
criterion = 0d0
do a = 1, nucl_num ! loop over the nuclei
tmp_int = 0d0
do i = 1, mo_num
do rho = 1, ao_num ! loop over all the AOs
do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
mu = nucl_aos(a,b)
tmp_int(i,i) = tmp_int(i,i) + 0.5d0 * (mo_coef(rho,i) * ao_overlap(rho,mu) * mo_coef(mu,i) &
+ mo_coef(mu,i) * ao_overlap(mu,rho) * mo_coef(rho,i))
enddo
enddo
enddo
do i = 1, mo_num
criterion = criterion + tmp_int(i,i)**2
enddo
enddo
criterion = - criterion
deallocate(tmp_int)
end
! Criterion PM
! The criterion is computed as
! \begin{align*}
! \mathcal{P} = \sum_{i=1}^n \sum_{A=1}^N \left[ <i|P_A|i> \right]^2
! \end{align*}
! with
! \begin{align*}
! <s|P_A|t> = \frac{1}{2} \sum_{\rho} \sum_{\mu \in A} \left[ c_{\rho}^{s*} S_{\rho \nu} c_{\mu}^{t} +c_{\mu}^{s*} S_{\mu \rho} c_{\rho}^t \right]
! \end{align*}
subroutine criterion_PM(tmp_list_size,tmp_list,criterion)
implicit none
BEGIN_DOC
! Compute the Pipek-Mezey localization criterion
END_DOC
integer, intent(in) :: tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: criterion
double precision, allocatable :: tmp_int(:,:),CS(:,:)
integer :: i,j,k,tmp_i,tmp_j,tmp_k, a, b, mu ,rho
print*,''
print*,'---criterion_PM---'
! Allocation
allocate(tmp_int(tmp_list_size, tmp_list_size),CS(mo_num,ao_num))
! Initialization
criterion = 0d0
call dgemm('T','N',mo_num,ao_num,ao_num,1d0,mo_coef,size(mo_coef,1),ao_overlap,size(ao_overlap,1),0d0,CS,size(CS,1))
do a = 1, nucl_num ! loop over the nuclei
tmp_int = 0d0
do tmp_i = 1, tmp_list_size
i = tmp_list(tmp_i)
do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
mu = nucl_aos(a,b)
tmp_int(tmp_i,tmp_i) = tmp_int(tmp_i,tmp_i) + 0.5d0 * (CS(i,mu) * mo_coef(mu,i) + mo_coef(mu,i) * CS(i,mu))
! (mo_coef(rho,i) * ao_overlap(rho,mu) * mo_coef(mu,j) &
!+ mo_coef(mu,i) * ao_overlap(mu,rho) * mo_coef(rho,j))
enddo
enddo
do tmp_i = 1, tmp_list_size
criterion = criterion + tmp_int(tmp_i,tmp_i)**2
enddo
enddo
criterion = - criterion
deallocate(tmp_int,CS)
print*,'---End criterion_PM---'
end
! Criterion PM v3
subroutine criterion_PM_v3(tmp_list_size,tmp_list,criterion)
implicit none
BEGIN_DOC
! Compute the Pipek-Mezey localization criterion
END_DOC
integer, intent(in) :: tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: criterion
double precision, allocatable :: tmp_int(:,:), CS(:,:), tmp_mo_coef(:,:), tmp_mo_coef2(:,:),tmp_accu(:,:),tmp_CS(:,:)
integer :: i,j,k,tmp_i,tmp_j,tmp_k, a, b, mu ,rho,nu,c
double precision :: t1,t2,t3
print*,''
print*,'---criterion_PM_v3---'
call wall_time(t1)
! Allocation
allocate(tmp_int(tmp_list_size, tmp_list_size),tmp_accu(tmp_list_size, tmp_list_size))
allocate(CS(tmp_list_size,ao_num),tmp_mo_coef(ao_num,tmp_list_size))
criterion = 0d0
! submatrix of the mo_coef
do tmp_i = 1, tmp_list_size
i = tmp_list(tmp_i)
do j = 1, ao_num
tmp_mo_coef(j,tmp_i) = mo_coef(j,i)
enddo
enddo
! ao_overlap(ao_num,ao_num)
! mo_coef(ao_num,mo_num)
call dgemm('T','N',tmp_list_size,ao_num,ao_num,1d0,tmp_mo_coef,size(tmp_mo_coef,1),ao_overlap,size(ao_overlap,1),0d0,CS,size(CS,1))
do a = 1, nucl_num ! loop over the nuclei
do j = 1, tmp_list_size
do i = 1, tmp_list_size
tmp_int(i,j) = 0d0
enddo
enddo
!do tmp_j = 1, tmp_list_size
! do tmp_i = 1, tmp_list_size
! do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
! mu = nucl_aos(a,b)
! tmp_int(tmp_i,tmp_j) = tmp_int(tmp_i,tmp_j) + 0.5d0 * (CS(tmp_i,mu) * tmp_mo_coef(mu,tmp_j) + tmp_mo_coef(mu,tmp_i) * CS(tmp_j,mu))
! ! (mo_coef(rho,i) * ao_overlap(rho,mu) * mo_coef(mu,j) &
! !+ mo_coef(mu,i) * ao_overlap(mu,rho) * mo_coef(rho,j))
! enddo
! enddo
!enddo
allocate(tmp_mo_coef2(nucl_n_aos(a),tmp_list_size),tmp_CS(tmp_list_size,nucl_n_aos(a)))
do tmp_i = 1, tmp_list_size
do b = 1, nucl_n_aos(a)
mu = nucl_aos(a,b)
tmp_mo_coef2(b,tmp_i) = tmp_mo_coef(mu,tmp_i)
enddo
enddo
do b = 1, nucl_n_aos(a)
mu = nucl_aos(a,b)
do tmp_i = 1, tmp_list_size
tmp_CS(tmp_i,b) = CS(tmp_i,mu)
enddo
enddo
call dgemm('N','N',tmp_list_size,tmp_list_size,nucl_n_aos(a),1d0,tmp_CS,size(tmp_CS,1),tmp_mo_coef2,size(tmp_mo_coef2,1),0d0,tmp_accu,size(tmp_accu,1))
! Integrals
do tmp_j = 1, tmp_list_size
do tmp_i = 1, tmp_list_size
tmp_int(tmp_i,tmp_j) = 0.5d0 * (tmp_accu(tmp_i,tmp_j) + tmp_accu(tmp_j,tmp_i))
enddo
enddo
deallocate(tmp_mo_coef2,tmp_CS)
! Criterion
do tmp_i = 1, tmp_list_size
criterion = criterion + tmp_int(tmp_i,tmp_i)**2
enddo
enddo
criterion = - criterion
deallocate(tmp_int,CS,tmp_accu,tmp_mo_coef)
call wall_time(t2)
t3 = t2 - t1
print*,'Time in criterion_PM_v3:', t3
print*,'---End criterion_PM_v3---'
end
! Criterion FB (old)
! The criterion is just computed as
! \begin{align*}
! C = - \sum_i^{mo_{num}} (<i|x|i>^2 + <i|y|i>^2 + <i|z|i>^2)
! \end{align*}
! The minus sign is here in order to minimize this criterion
! Output:
! | criterion | double precision | criterion for the Foster-Boys localization |
subroutine criterion_FB_old(criterion)
implicit none
BEGIN_DOC
! Compute the Foster-Boys localization criterion
END_DOC
double precision, intent(out) :: criterion
integer :: i
! Criterion (= \sum_i <i|r|i>^2 )
criterion = 0d0
do i = 1, mo_num
criterion = criterion + mo_dipole_x(i,i)**2 + mo_dipole_y(i,i)**2 + mo_dipole_z(i,i)**2
enddo
criterion = - criterion
end subroutine
! Criterion FB
subroutine criterion_FB(tmp_list_size, tmp_list, criterion)
implicit none
BEGIN_DOC
! Compute the Foster-Boys localization criterion
END_DOC
integer, intent(in) :: tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(out) :: criterion
integer :: i, tmp_i
! Criterion (= - \sum_i <i|r|i>^2 )
criterion = 0d0
do tmp_i = 1, tmp_list_size
i = tmp_list(tmp_i)
criterion = criterion + mo_dipole_x(i,i)**2 + mo_dipole_y(i,i)**2 + mo_dipole_z(i,i)**2
enddo
criterion = - criterion
end subroutine
subroutine theta_FB(l, n, m_x, max_elem)
include 'pi.h'
BEGIN_DOC
! Compute the angles to minimize the Foster-Boys criterion by using pairwise rotations of the MOs
! Warning: you must give - the angles to build the rotation matrix...
END_DOC
implicit none
integer, intent(in) :: n, l(n)
double precision, intent(out) :: m_x(n,n), max_elem
integer :: i,j, tmp_i, tmp_j
double precision, allocatable :: cos4theta(:,:), sin4theta(:,:)
double precision, allocatable :: A(:,:), B(:,:), beta(:,:), gamma(:,:)
integer :: idx_i,idx_j
allocate(cos4theta(n, n), sin4theta(n, n))
allocate(A(n,n), B(n,n), beta(n,n), gamma(n,n))
do tmp_j = 1, n
j = l(tmp_j)
do tmp_i = 1, n
i = l(tmp_i)
A(tmp_i,tmp_j) = mo_dipole_x(i,j)**2 - 0.25d0 * (mo_dipole_x(i,i) - mo_dipole_x(j,j))**2 &
+ mo_dipole_y(i,j)**2 - 0.25d0 * (mo_dipole_y(i,i) - mo_dipole_y(j,j))**2 &
+ mo_dipole_z(i,j)**2 - 0.25d0 * (mo_dipole_z(i,i) - mo_dipole_z(j,j))**2
enddo
A(j,j) = 0d0
enddo
do tmp_j = 1, n
j = l(tmp_j)
do tmp_i = 1, n
i = l(tmp_i)
B(tmp_i,tmp_j) = mo_dipole_x(i,j) * (mo_dipole_x(i,i) - mo_dipole_x(j,j)) &
+ mo_dipole_y(i,j) * (mo_dipole_y(i,i) - mo_dipole_y(j,j)) &
+ mo_dipole_z(i,j) * (mo_dipole_z(i,i) - mo_dipole_z(j,j))
enddo
enddo
!do tmp_j = 1, n
! j = l(tmp_j)
! do tmp_i = 1, n
! i = l(tmp_i)
! beta(tmp_i,tmp_j) = (mo_dipole_x(i,i) - mo_dipole_x(j,j)) - 4d0 * mo_dipole_x(i,j)**2 &
! + (mo_dipole_y(i,i) - mo_dipole_y(j,j)) - 4d0 * mo_dipole_y(i,j)**2 &
! + (mo_dipole_z(i,i) - mo_dipole_z(j,j)) - 4d0 * mo_dipole_z(i,j)**2
! enddo
!enddo
!do tmp_j = 1, n
! j = l(tmp_j)
! do tmp_i = 1, n
! i = l(tmp_i)
! gamma(tmp_i,tmp_j) = 4d0 * ( mo_dipole_x(i,j) * (mo_dipole_x(i,i) - mo_dipole_x(j,j)) &
! + mo_dipole_y(i,j) * (mo_dipole_y(i,i) - mo_dipole_y(j,j)) &
! + mo_dipole_z(i,j) * (mo_dipole_z(i,i) - mo_dipole_z(j,j)))
! enddo
!enddo
!
!do j = 1, n
! do i = 1, n
! cos4theta(i,j) = - A(i,j) / dsqrt(A(i,j)**2 + B(i,j)**2)
! enddo
!enddo
!do j = 1, n
! do i = 1, n
! sin4theta(i,j) = B(i,j) / dsqrt(A(i,j)**2 + B(i,j)**2)
! enddo
!enddo
! Theta
do j = 1, n
do i = 1, n
m_x(i,j) = 0.25d0 * atan2(B(i,j), -A(i,j))
!m_x(i,j) = 0.25d0 * atan2(sin4theta(i,j), cos4theta(i,j))
enddo
enddo
! Enforce a perfect antisymmetry
do j = 1, n-1
do i = j+1, n
m_x(j,i) = - m_x(i,j)
enddo
enddo
do i = 1, n
m_x(i,i) = 0d0
enddo
! Max
max_elem = 0d0
do j = 1, n-1
do i = j+1, n
if (dabs(m_x(i,j)) > dabs(max_elem)) then
max_elem = m_x(i,j)
!idx_i = i
!idx_j = j
endif
enddo
enddo
! Debug
!print*,''
!print*,'sin/B'
!do i = 1, n
! write(*,'(100F10.4)') sin4theta(i,:)
! !B(i,:)
!enddo
!print*,'cos/A'
!do i = 1, n
! write(*,'(100F10.4)') cos4theta(i,:)
! !A(i,:)
!enddo
!print*,'X'
!!m_x = 0d0
!!m_x(idx_i,idx_j) = max_elem
!!m_x(idx_j,idx_i) = -max_elem
!do i = 1, n
! write(*,'(100F10.4)') m_x(i,:)
!enddo
!print*,idx_i,idx_j,max_elem
max_elem = dabs(max_elem)
deallocate(cos4theta, sin4theta)
deallocate(A,B,beta,gamma)
end
subroutine theta_PM(l, n, m_x, max_elem)
include 'pi.h'
BEGIN_DOC
! Compute the angles to minimize the Foster-Boys criterion by using pairwise rotations of the MOs
! Warning: you must give - the angles to build the rotation matrix...
END_DOC
implicit none
integer, intent(in) :: n, l(n)
double precision, intent(out) :: m_x(n,n), max_elem
integer :: a,b,i,j,tmp_i,tmp_j,rho,mu,nu,idx_i,idx_j
double precision, allocatable :: Aij(:,:), Bij(:,:), Pa(:,:)
allocate(Aij(n,n), Bij(n,n), Pa(n,n))
do a = 1, nucl_num ! loop over the nuclei
Pa = 0d0 ! Initialization for each nuclei
! Loop over the MOs of the a given mo_class to compute <i|P_a|j>
do tmp_j = 1, n
j = l(tmp_j)
do tmp_i = 1, n
i = l(tmp_i)
do rho = 1, ao_num ! loop over all the AOs
do b = 1, nucl_n_aos(a) ! loop over the number of AOs which belongs to the nuclei a
mu = nucl_aos(a,b) ! AO centered on atom a
Pa(tmp_i,tmp_j) = Pa(tmp_i,tmp_j) + 0.5d0 * (mo_coef(rho,i) * ao_overlap(rho,mu) * mo_coef(mu,j) &
+ mo_coef(mu,i) * ao_overlap(mu,rho) * mo_coef(rho,j))
enddo
enddo
enddo
enddo
! A
do j = 1, n
do i = 1, n
Aij(i,j) = Aij(i,j) + Pa(i,j)**2 - 0.25d0 * (Pa(i,i) - Pa(j,j))**2
enddo
enddo
! B
do j = 1, n
do i = 1, n
Bij(i,j) = Bij(i,j) + Pa(i,j) * (Pa(i,i) - Pa(j,j))
enddo
enddo
enddo
! Theta
do j = 1, n
do i = 1, n
m_x(i,j) = 0.25d0 * atan2(Bij(i,j), -Aij(i,j))
enddo
enddo
! Enforce a perfect antisymmetry
do j = 1, n-1
do i = j+1, n
m_x(j,i) = - m_x(i,j)
enddo
enddo
do i = 1, n
m_x(i,i) = 0d0
enddo
! Max
max_elem = 0d0
do j = 1, n-1
do i = j+1, n
if (dabs(m_x(i,j)) > dabs(max_elem)) then
max_elem = m_x(i,j)
idx_i = i
idx_j = j
endif
enddo
enddo
! Debug
!do i = 1, n
! write(*,'(100F10.4)') m_x(i,:)
!enddo
!print*,'Max',idx_i,idx_j,max_elem
max_elem = dabs(max_elem)
deallocate(Aij,Bij,Pa)
end
! Spatial extent
! The spatial extent of an orbital $i$ is computed as
! \begin{align*}
! \sum_{\lambda=x,y,z}\sqrt{<i|\lambda^2|i> - <i|\lambda|i>^2}
! \end{align*}
! From that we can also compute the average and the standard deviation
subroutine compute_spatial_extent(spatial_extent)
implicit none
BEGIN_DOC
! Compute the spatial extent of the MOs
END_DOC
double precision, intent(out) :: spatial_extent(mo_num)
double precision :: average_core, average_act, average_inact, average_virt
double precision :: std_var_core, std_var_act, std_var_inact, std_var_virt
integer :: i,j,k,l
spatial_extent = 0d0
do i = 1, mo_num
spatial_extent(i) = mo_spread_x(i,i) - mo_dipole_x(i,i)**2
enddo
do i = 1, mo_num
spatial_extent(i) = spatial_extent(i) + mo_spread_y(i,i) - mo_dipole_y(i,i)**2
enddo
do i = 1, mo_num
spatial_extent(i) = spatial_extent(i) + mo_spread_z(i,i) - mo_dipole_z(i,i)**2
enddo
do i = 1, mo_num
spatial_extent(i) = dsqrt(spatial_extent(i))
enddo
average_core = 0d0
std_var_core = 0d0
if (dim_list_core_orb >= 2) then
call compute_average_sp_ext(spatial_extent, list_core, dim_list_core_orb, average_core)
call compute_std_var_sp_ext(spatial_extent, list_core, dim_list_core_orb, average_core, std_var_core)
endif
average_act = 0d0
std_var_act = 0d0
if (dim_list_act_orb >= 2) then
call compute_average_sp_ext(spatial_extent, list_act, dim_list_act_orb, average_act)
call compute_std_var_sp_ext(spatial_extent, list_act, dim_list_act_orb, average_act, std_var_act)
endif
average_inact = 0d0
std_var_inact = 0d0
if (dim_list_inact_orb >= 2) then
call compute_average_sp_ext(spatial_extent, list_inact, dim_list_inact_orb, average_inact)
call compute_std_var_sp_ext(spatial_extent, list_inact, dim_list_inact_orb, average_inact, std_var_inact)
endif
average_virt = 0d0
std_var_virt = 0d0
if (dim_list_virt_orb >= 2) then
call compute_average_sp_ext(spatial_extent, list_virt, dim_list_virt_orb, average_virt)
call compute_std_var_sp_ext(spatial_extent, list_virt, dim_list_virt_orb, average_virt, std_var_virt)
endif
print*,''
print*,'============================='
print*,' Spatial extent of the MOs'
print*,'============================='
print*,''
print*, 'elec_num:', elec_num
print*, 'elec_alpha_num:', elec_alpha_num
print*, 'elec_beta_num:', elec_beta_num
print*, 'core:', dim_list_core_orb
print*, 'act:', dim_list_act_orb
print*, 'inact:', dim_list_inact_orb
print*, 'virt:', dim_list_virt_orb
print*, 'mo_num:', mo_num
print*,''
print*,'-- Core MOs --'
print*,'Average:', average_core
print*,'Std var:', std_var_core
print*,''
print*,'-- Active MOs --'
print*,'Average:', average_act
print*,'Std var:', std_var_act
print*,''
print*,'-- Inactive MOs --'
print*,'Average:', average_inact
print*,'Std var:', std_var_inact
print*,''
print*,'-- Virtual MOs --'
print*,'Average:', average_virt
print*,'Std var:', std_var_virt
print*,''
print*,'Spatial extent:'
do i = 1, mo_num
print*, i, spatial_extent(i)
enddo
end
subroutine compute_average_sp_ext(spatial_extent, list, list_size, average)
implicit none
BEGIN_DOC
! Compute the average spatial extent of the MOs
END_DOC
integer, intent(in) :: list_size, list(list_size)
double precision, intent(in) :: spatial_extent(mo_num)
double precision, intent(out) :: average
integer :: i, tmp_i
average = 0d0
do tmp_i = 1, list_size
i = list(tmp_i)
average = average + spatial_extent(i)
enddo
average = average / DBLE(list_size)
end
subroutine compute_std_var_sp_ext(spatial_extent, list, list_size, average, std_var)
implicit none
BEGIN_DOC
! Compute the standard deviation of the spatial extent of the MOs
END_DOC
integer, intent(in) :: list_size, list(list_size)
double precision, intent(in) :: spatial_extent(mo_num)
double precision, intent(in) :: average
double precision, intent(out) :: std_var
integer :: i, tmp_i
std_var = 0d0
do tmp_i = 1, list_size
i = list(tmp_i)
std_var = std_var + (spatial_extent(i) - average)**2
enddo
std_var = dsqrt(1d0/DBLE(list_size) * std_var)
end
! Utils
subroutine apply_pre_rotation()
implicit none
BEGIN_DOC
! Apply a rotation between the MOs
END_DOC
double precision, allocatable :: pre_rot(:,:), prev_mos(:,:), R(:,:)
double precision :: t1,t2,t3
integer :: i,j,tmp_i,tmp_j
integer :: info
logical :: enforce_step_cancellation
print*,'---apply_pre_rotation---'
call wall_time(t1)
allocate(pre_rot(mo_num,mo_num), prev_mos(ao_num,mo_num), R(mo_num,mo_num))
! Initialization of the matrix
pre_rot = 0d0
if (kick_in_mos) then
! Pre rotation for core MOs
if (dim_list_core_orb >= 2) then
do tmp_j = 1, dim_list_core_orb
j = list_core(tmp_j)
do tmp_i = 1, dim_list_core_orb
i = list_core(tmp_i)
if (i > j) then
pre_rot(i,j) = angle_pre_rot
elseif (i < j) then
pre_rot(i,j) = - angle_pre_rot
else
pre_rot(i,j) = 0d0
endif
enddo
enddo
endif
! Pre rotation for active MOs
if (dim_list_act_orb >= 2) then
do tmp_j = 1, dim_list_act_orb
j = list_act(tmp_j)
do tmp_i = 1, dim_list_act_orb
i = list_act(tmp_i)
if (i > j) then
pre_rot(i,j) = angle_pre_rot
elseif (i < j) then
pre_rot(i,j) = - angle_pre_rot
else
pre_rot(i,j) = 0d0
endif
enddo
enddo
endif
! Pre rotation for inactive MOs
if (dim_list_inact_orb >= 2) then
do tmp_j = 1, dim_list_inact_orb
j = list_inact(tmp_j)
do tmp_i = 1, dim_list_inact_orb
i = list_inact(tmp_i)
if (i > j) then
pre_rot(i,j) = angle_pre_rot
elseif (i < j) then
pre_rot(i,j) = - angle_pre_rot
else
pre_rot(i,j) = 0d0
endif
enddo
enddo
endif
! Pre rotation for virtual MOs
if (dim_list_virt_orb >= 2) then
do tmp_j = 1, dim_list_virt_orb
j = list_virt(tmp_j)
do tmp_i = 1, dim_list_virt_orb
i = list_virt(tmp_i)
if (i > j) then
pre_rot(i,j) = angle_pre_rot
elseif (i < j) then
pre_rot(i,j) = - angle_pre_rot
else
pre_rot(i,j) = 0d0
endif
enddo
enddo
endif
! Nothing for deleted ones
! Compute pre rotation matrix from pre_rot
call rotation_matrix(pre_rot,mo_num,R,mo_num,mo_num,info,enforce_step_cancellation)
if (enforce_step_cancellation) then
print*, 'Cancellation of the pre rotation, too big error in the rotation matrix'
print*, 'Reduce the angle for the pre rotation, abort'
call abort
endif
! New Mos (we don't car eabout the previous MOs prev_mos)
call apply_mo_rotation(R,prev_mos)
! Update the things related to mo_coef
TOUCH mo_coef
call save_mos
endif
deallocate(pre_rot, prev_mos, R)
call wall_time(t2)
t3 = t2-t1
print*,'Time in apply_pre_rotation:', t3
print*,'---End apply_pre_rotation---'
end
subroutine x_tmp_orb_loc_v2(tmp_n, tmp_list_size, tmp_list, v_grad, H,tmp_x, tmp_m_x)
implicit none
integer, intent(in) :: tmp_n, tmp_list_size, tmp_list(tmp_list_size)
double precision, intent(in) :: v_grad(tmp_n)
double precision, intent(in) :: H(tmp_n, tmp_n)
double precision, intent(out) :: tmp_m_x(tmp_list_size, tmp_list_size), tmp_x(tmp_list_size)
!double precision, allocatable :: x(:)
double precision :: lambda , accu, max_elem
integer :: i,j,tmp_i,tmp_j,tmp_k
! Allocation
!allocate(x(tmp_n))
! Level shifted hessian
lambda = 0d0
do tmp_k = 1, tmp_n
if (H(tmp_k,tmp_k) < lambda) then
lambda = H(tmp_k,tmp_k)
endif
enddo
! min element in the hessian
if (lambda < 0d0) then
lambda = -lambda + 1d-6
endif
print*, 'lambda', lambda
! Good
do tmp_k = 1, tmp_n
if (ABS(H(tmp_k,tmp_k)) > 1d-6) then
tmp_x(tmp_k) = - 1d0/(ABS(H(tmp_k,tmp_k))+lambda) * v_grad(tmp_k)!(-v_grad(tmp_k))
!x(tmp_k) = - 1d0/(ABS(H(tmp_k,tmp_k))+lambda) * (-v_grad(tmp_k))
endif
enddo
! 1D tmp -> 2D tmp
tmp_m_x = 0d0
do tmp_j = 1, tmp_list_size - 1
do tmp_i = tmp_j + 1, tmp_list_size
call mat_to_vec_index(tmp_i,tmp_j,tmp_k)
tmp_m_x(tmp_i, tmp_j) = tmp_x(tmp_k)!x(tmp_k)
enddo
enddo
! Antisym
do tmp_i = 1, tmp_list_size - 1
do tmp_j = tmp_i + 1, tmp_list_size
tmp_m_x(tmp_i,tmp_j) = - tmp_m_x(tmp_j,tmp_i)
enddo
enddo
! Deallocation
!deallocate(x)
end subroutine
subroutine ao_to_mo_no_sym(A_ao,LDA_ao,A_mo,LDA_mo)
implicit none
BEGIN_DOC
! Transform A from the |AO| basis to the |MO| basis
!
! $C^\dagger.A_{ao}.C$
END_DOC
integer, intent(in) :: LDA_ao,LDA_mo
double precision, intent(in) :: A_ao(LDA_ao,ao_num)
double precision, intent(out) :: A_mo(LDA_mo,mo_num)
double precision, allocatable :: T(:,:)
allocate ( T(ao_num,mo_num) )
!DIR$ ATTRIBUTES ALIGN : $IRP_ALIGN :: T
call dgemm('N','N', ao_num, mo_num, ao_num, &
1.d0, A_ao,LDA_ao, &
mo_coef, size(mo_coef,1), &
0.d0, T, size(T,1))
call dgemm('T','N', mo_num, mo_num, ao_num, &
1.d0, mo_coef,size(mo_coef,1), &
T, ao_num, &
0.d0, A_mo, size(A_mo,1))
deallocate(T)
end
subroutine run_sort_by_fock_energies()
implicit none
BEGIN_DOC
! Saves the current MOs ordered by diagonal element of the Fock operator.
END_DOC
integer :: i,j,k,l,tmp_i,tmp_k,tmp_list_size
integer, allocatable :: iorder(:), tmp_list(:)
double precision, allocatable :: fock_energies_tmp(:), tmp_mo_coef(:,:)
! Test
do l = 1, 4
if (l==1) then ! core
tmp_list_size = dim_list_core_orb
elseif (l==2) then ! act
tmp_list_size = dim_list_act_orb
elseif (l==3) then ! inact
tmp_list_size = dim_list_inact_orb
else ! virt
tmp_list_size = dim_list_virt_orb
endif
if (tmp_list_size >= 2) then
! Allocation tmp array
allocate(tmp_list(tmp_list_size))
! To give the list of MOs in a mo_class
if (l==1) then ! core
tmp_list = list_core
elseif (l==2) then
tmp_list = list_act
elseif (l==3) then
tmp_list = list_inact
else
tmp_list = list_virt
endif
print*,'MO class: ',trim(mo_class(tmp_list(1)))
allocate(iorder(tmp_list_size), fock_energies_tmp(tmp_list_size), tmp_mo_coef(ao_num,tmp_list_size))
!print*,'MOs before sorting them by f_p^p energies:'
do i = 1, tmp_list_size
tmp_i = tmp_list(i)
fock_energies_tmp(i) = Fock_matrix_diag_mo(tmp_i)
iorder(i) = i
!print*, tmp_i, fock_energies_tmp(i)
enddo
call dsort(fock_energies_tmp, iorder, tmp_list_size)
print*,'MOs after sorting them by f_p^p energies:'
do i = 1, tmp_list_size
k = iorder(i)
tmp_k = tmp_list(k)
print*, tmp_k, fock_energies_tmp(k)
do j = 1, ao_num
tmp_mo_coef(j,k) = mo_coef(j,tmp_k)
enddo
enddo
! Update the MOs after sorting them by energies
do i = 1, tmp_list_size
tmp_i = tmp_list(i)
do j = 1, ao_num
mo_coef(j,tmp_i) = tmp_mo_coef(j,i)
enddo
enddo
if (debug_hf) then
touch mo_coef
print*,'HF energy:', HF_energy
endif
print*,''
deallocate(iorder, fock_energies_tmp, tmp_list, tmp_mo_coef)
endif
enddo
touch mo_coef
call save_mos
end
function is_core(i)
implicit none
BEGIN_DOC
! True if the orbital i is a core orbital
END_DOC
integer, intent(in) :: i
logical :: is_core
integer :: j
! Init
is_core = .False.
! Search
do j = 1, dim_list_core_orb
if (list_core(j) == i) then
is_core = .True.
exit
endif
enddo
end
function is_del(i)
implicit none
BEGIN_DOC
! True if the orbital i is a deleted orbital
END_DOC
integer, intent(in) :: i
logical :: is_del
integer :: j
! Init
is_del = .False.
! Search
do j = 1, dim_list_core_orb
if (list_core(j) == i) then
is_del = .True.
exit
endif
enddo
end
subroutine set_classes_loc()
implicit none
integer :: i
logical :: ok1, ok2
logical :: is_core, is_del
integer(bit_kind) :: res(N_int,2)
if (auto_mo_class) then
do i = 1, mo_num
if (is_core(i)) cycle
if (is_del(i)) cycle
call apply_hole(psi_det(1,1,1), 1, i, res, ok1, N_int)
call apply_hole(psi_det(1,1,1), 2, i, res, ok2, N_int)
if (ok1 .and. ok2) then
mo_class(i) = 'Inactive'
else if (.not. ok1 .and. .not. ok2) then
mo_class(i) = 'Virtual'
else
mo_class(i) = 'Active'
endif
enddo
touch mo_class
endif
end
subroutine unset_classes_loc()
implicit none
integer :: i
logical :: ok1, ok2
logical :: is_core, is_del
integer(bit_kind) :: res(N_int,2)
if (auto_mo_class) then
do i = 1, mo_num
if (is_core(i)) cycle
if (is_del(i)) cycle
mo_class(i) = 'Active'
enddo
touch mo_class
endif
end